Chapter 32, Problem 22PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

# Naturally occurring 40K is listed as responsible for 16 mrem/y of background radiation. Calculate the mass of 40K that must be inside the 55−kg body of a woman to produce this dose. Each 40K decay emits a 1.32−MeV β, and 50% of the energy is absorbed inside the body.

To determine

The mass of 40K that must be inside a 55 kg body of a woman to produce a dose of 16 mrem/y of background radiation if 50% of the energy is absorbed by the body.

Explanation

Given info:

â€ƒâ€ƒdose=16Â mrem/y

Mass of the woman's body

â€ƒâ€ƒm=55Â kg

Energy of the emitted Î² particle

â€ƒâ€ƒEÎ²=1.32MeV

Half-life of 40K

â€ƒâ€ƒt1/2=1.251Ã—109y

Formula used:

The activity of a radioactive sample is given by,

â€ƒâ€ƒR=0.693Nt1/2

Here, N is the number of atoms of the radioactive substance present.

The dose in rem is related to the dose in rad as follows:

â€ƒâ€ƒdoseÂ inÂ rem=Â doseÂ inÂ radÃ—RBE

Here RBE is the relative biological effectiveness.

Calculation:

The RBE for Î² particle is 1.

Therefore,

Express the dose per year in J/kg.

The energy deposited in the woman for the radiation of the energy for a year as calculated above is given by,

Therefore,

â€ƒâ€ƒE=radiationÂ doseÃ—massÂ ofÂ theÂ woman=1.60Ã— 10 âˆ’4J/kgâ‹…y55Â kg=8.80Ã—10âˆ’3J/y

Express the energy in MeV/y.

â€ƒâ€ƒE=8.80Ã—10âˆ’3J/yÃ—1Â MeV1.6Ã— 10 âˆ’13J=5

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